The present invention relates generally to the filtering, e.g., wavelet filtering, of n-dimensional signals, images or arrays (hereinafter: signals), for the purposes of signal decomposition, enhancement, compression, restoration, denoising, segmentation, feature extraction and target/object/surface detection/recognition. The analysis method of the invention provides a complete omnidirectional (0-180 degrees) but yet one-dimensional (1D) filtering method for two-dimensional (2D) images that is superior to the methods of prior art. The methods of prior art either bias the filtering process in the horizontal, vertical and diagonal directions of the image, or depart from filter definitions in adopting a circular form.
The methods described here permit the construction of microprocessors that allow certain operations to be done in hardware. Those operations are (1) a Radon transform of the image(s) or array(s)—we shall refer to the transformed image as the projection space version of the image; and (2) convolution of the Fourier transform of the 1D filters, e.g., wavelet filters, with a 1D Ram-Lak, or other bandlimited filter—the resultant of the convolutions we refer to as the resultant 1D filters; (3) convolution of the resultant 1D filters with each of the 1D columns of the 2D Radon transform or projection space version of the image; and (4) an inverse Radon transform of the now omnidirectionally filtered projection space version of the image, either directly or after transmission.